简便计算奥数题(1-1/18-1/19)*(1/17+1/18)+(1/18+1/19)*(1/17+1/18-1)用代数法,设两个数

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简便计算奥数题(1-1/18-1/19)*(1/17+1/18)+(1/18+1/19)*(1/17+1/18-1)用代数法,设两个数
简便计算奥数题
(1-1/18-1/19)*(1/17+1/18)+(1/18+1/19)*(1/17+1/18-1)
用代数法,设两个数

简便计算奥数题(1-1/18-1/19)*(1/17+1/18)+(1/18+1/19)*(1/17+1/18-1)用代数法,设两个数
设x=1/18+1/19,y=1/17+1/18
原式=(1-x)*y+x*(y-1)=y-xy+xy-x=y-x=1/17-1/19=2/323

(1-1/18-1/19)*(1/17+1/18)+(1/18+1/19)*(1/17+1/18-1)
=[1-(1/18+1/19)]*(1/17+1/18)+(1/18+1/19)*(1/17+1/18-1)
=(1/17+1/18)- (1/18+1/19)*(1/17+1/18)+(1/18+1/19)*(1/17+1/18)-(1/18+1/19)
=(1/17+1/18)- (1/18+1/19)
=1/17+1/18- 1/18-1/19
=......